On Monday, Alexis shot and killed 12 people during a shooting spree at the Navy's Washington, D.C., headquarters before being killed by law enforcement during the daylong stand off.
Defense officials say Alexis obtained a security clearance while he was in the Navy and was not subjected to a second background check when he became a contractor after leaving the service in 2011.
Part of the Pentagon's decision not to reinvestigate Alexis's security clearance may have stemmed from his honorable discharge from the Navy, according to Ayotte.
"Had Alexis received a general discharge, future employers would have been more likely to give his background extra scrutiny," Ayotte wrote.
"This additional scrutiny may have helped potential employers identify Alexis’ reported arrests in three states and better informed their hiring decisions," she added.
Specifically, Ayotte wants information on whether a former service member's discharge status plays a role in how the Navy selects its contractor workforce.
If a former service member receives anything other than an honorable discharge, "what additional scrutiny or steps does this trigger under current procedures?" Ayotte asked in the letter.
That said, the New Hampshire Republican openly questioned the Navy's decision to grant Alexis a honorable discharge, given the former sailor's troubled Navy career.
While in the Navy, Alexis was reportedly arrested on misdemeanor weapons charges in Fort Worth, Texas, which led to him leaving the service in 2011.
Despite his criminal record, Alexis was hired as a Navy information technology contractor, based at the Navy Yard.
After his discharge, Alexis twice checked into emergency rooms at different VA medical centers in August, five days apart, The Hill reported Wednesday.
Alexis was treated by the VA in Rhode Island and again in Washington, D.C., for insomnia, and was prescribed medication.
For their part, Pentagon officials claim reinvestigations for security clearances could be triggered when a former military member is transitioning into contractor or civilian service.
But that only occurs if the time between retirement and re-entry is more than two years and if “derogatory information” is uncovered, officials say.